Act on collective emergent phenomena with the purpose to change, regulate and maintain acquired properties;

Merge differentcollective emergent phenomena.

The core ideas of the project, considering emergence as mesoscopic coherenceandcollective behaviours as coherent sequences of different systems,in short, are:

1.1 Multiple systems

A Multiple System (MS) [Minati, 2006] is a set of systems established by the same components interacting in different ways, i.e., having multiple simultaneous or dynamical roles. In this way the same interacting components may simultaneously and/or sequentially establish different systems. Examples of MSs are given by networked interacting computer systems performing multiple tasks as on the Internet, or by electricity networks where different systems play different roles

1.2 Collective beings

Collective Beings (CBs) [Minati & Pessa, 2006, pp.97-137] are particular cases of MSs when considered to be established by agents possessing a cognitive system allowing multiple roles be active, i.e., decided by the component autonomous agents. Examples of CBs are Human Social Systems when autonomous agents a) simultaneouslygenerate and belong to different systems, e.g., they simultaneously behave as buyers in a market and components of communities such as mobile telephone networks and families and traffic systems and workplaces, and/or dynamically give rise to different systems, e.g., audience, passengers on trains or in queues. Multiple simultaneous or dynamical roles of MSs and CBs are modelled by using ergodicity [Minati, 2002; Minati & Pessa, 2006, pp. 300-313].

1.3 Logical Openess

Logical Openness is conceptually different from classical thermodynamic openness (Minati et al., 1998;Minati&Pessa, 2006) dealing with the exchange of matter and energy. Logical Openness relates to the constructivist role [Von Glasersfeld, 1995] of the observer generating n-levels ofmodels (meta-modelling) by

simultaneously representing one level through another allowing decisions, for instance, through correspondences and simulations;

Simultaneously considering more than one level as in the Dynamic Usage of Models (DYSAM).

Logical openness relates to the theoretically active role of the observer self-generating and simultaneously using several levels of description rather than selecting a single one considered as the best among available choices. It is possible to introduce a hierarchy of logically open models based on suitable openness levels.

1.4 DYSAM

DYSAM (Minati & Brahms, 2002; Minati & Pessa, 2006) as meta-modeling, i.e., modeling models, is based on strategies to select, invent and use models for decision making. DYSAM is based on strategies using independent and irreducible models as in well-established approaches such as the Bayesian method, Ensemble Learning, Evolutionary Game Theory,Machine Learning and Pierce’s abduction. Models may be corporate models, theories of management, approaches and methodologies used , for instance, with industrial districts when business relationships are simultaneously competitive and cooperative as in the notion of "co-opetition", and soft-systems methodologieswith their specific level of description. While pragmatism is event-driven, DYSAM is theoretically observer-driven. The conceptual difference lies in the effectiveness of coherence between models, i.e., systems of models.

1.5 Complexity

Complexity deals with phenomena where processes of emergence occur within them, i.e., acquisitions of properties not computable from the previous ones. It means that they may be represented, recognised, induced and changed only by using different, non-equivalent models. It relates, for instance, to emergence of coherent sequences of configurations of elements [Minati and Licata, submitted]. This is why the process cannot be suitably modelled by using a single model, but, rather, by a sequence of non equivalent models and without assuming completeness of the modelling. In this way a process of emergence is always logically open. Multiple Systems, Collective Beings, Logical openness and DYSAM are aspects ofr complex phenomena.

Another approach is based on considering processes of emergence given by phenomena of bifurcationassociated with the ones of Symmetry System Breaking (SSB).

The term bifurcation relates to a change in the number or type of attractors as a consequence of changes in parameter values. The concept is applied to systems whose evolution equations also contain a number of parameters, i.e., quantities whose value can vary, not as an effect of the state of the system itself, but only under the influence of an external environment.

Wehave symmetry breaking when a symmetry transformation leaves the form of the evolution equations invariant, but changes the form of their solutions. A typical example is that of a sample of matter consisting of atoms which, at a given temperature, is paramagnetic. If the temperature is decreased, there is a critical point (the so-called Curie point) where a transition from the paramagnetic to the ferromagnetic phase occurs, i.e. a phase transition. This gives rise to an internal magnetic field of macroscopic dimensions, deriving from the alignment of the magnetic fields of the individual atoms due to their interactions. The presence of such a field leads to the existence of a preferred direction, i.e., that of the internal magnetic field. Thus, although the form of the equations describing the motions of the atoms continues to be invariant with respect to the symmetry transformations constituted by spatial rotations, their solutions are not, as the preferred direction breaks such invariance [Minati and Pessa, 1996; Anderson 1981; Anderson and Stein 1985] .

In the approach based on Meta-Structures we consider the occurring of Dynamic Structure and their coherence as suitable general way to model complexity.

1.6 Dynamic Structures

Fixed analytical representations of rules of interaction between microscopic or macroscopic state variables used to model dynamical system are assumed to be the structures of the system, e.g., the Brusselator, Lorenz or Lotka-Volterra equations. In our approach dynamics does not refer to the presence of time in equations of the model, but, rather, on the change in time of models themselves, even dynamic in the classical sense, and representing change of structures of the system over time.

The term Meta-Structure relates to a coherent change of structures allowing continuous emergence of the same of different acquired properties, such as properties of swarms and flocks.In this project we consider the structures between microscopic or macroscopic variables as variable, i.e., the analytical representations of rules of interaction change over time as well the elements to which those rules are applied. Dynamic structures are assumed to change over time in such a way as to cause Collective Behaviour to emerge from Collective Interactions.

The approach based on Meta-Structures considers processes of emergence as sequences of states adopted by different single systems which may exist for any period of time and which consist of the same elements interacting in different ways over time. These sequences are considered coherent when intended as corresponding to states adopted by an entity, such as coherent Multiple Systems and Collective Beings introduced below, acquiring and maintaining emergent properties. This coherence is proposed here as being suitably modelled by Meta-Structural properties [Minati, 2008a; 2008b; 2008c; 2009a; 20089b ].

1.7 Coherence

In our approach we consider a concept of coherence different from the one used in classical physics. For instance, in physics the coherence of two waves relates to how well correlated they are as quantified by the cross-correlation function quantifying the possibility to predict the value of the second wave by knowing the value of the first. It is also possible to consider self-coherence when the second wave is not a separate one, but always the first wave at a different time or position. In this case the measure of correlation is the autocorrelation function.

We consider here coherence [Mikhailovand Calenbuhr, 2002] as the maintenance of the same acquired property by collective interacting elements over time. The same property of systems is allowed by processes of interaction between constituting elements by using the same structure. In the case considered here we have sequences of structures establishing a system when coherent.

The kind of coherence considered here is intended as dynamic regularity and represented by the values adopted by suitable mesoscopic variables and their properties, i.e., meta-structural properties.

In particular,we consider here coherence in Self-organisation due to properties, such as regularities and quasi-periodicities, of microscopic and macroscopic variables. Coherence in Emergence is considereddue to properties, such as regularities and quasi-periodicities, of mesoscopic variables [Minati, 2008c].

Table 1. Processes of Phase transition and Self-organisation compared with reference to structure and acquisition of properties.

Phase transition as change of structure

Self-organisation: Variability of the structure is stable, i.e. repetitive and foreseeable

Change of structure, like assumption of a new one or lose of any structure (e.g., gas) corresponding to the acquisition of a new property. Examples of phase transitions, i.e. changes of structure, in social systems are revolutions and learning in cognitive systems. Phase transitions occur in presence of external changes.

External input starts a new structure.

Variability of the structure of a process of self-organisation is stable, i.e. repetitive and foreseeable. Stability of variability corresponds to stability of the acquired property. For instance, swarms having repetitive behaviour, laser, ferromagnetism and superconductivity and dissipative structures, like whirlpools in absence of any internal or external fluctuation.

Variability is allowed by thermodynamic openness.

Correspondence between structure and acquired property

1.8 Emergence

Processes of emergence occurring in collectively interacting elements relates to acquisitions of properties not computable from previous ones possessed by elements or systems established by them. It means that the observer must use different, non-equivalent models. Particularly it possible to consider a kind of hierarchy of emergence [Cruchtfield, 1994], from the simplest to the more complex by considering the nature and its of modelling required as well its theoretical incompleteness [Minati and Pessa, 1996]:

One kind of emergence is named computational emergence. It relates to processes of establishment of unexpected effects by using a specific model. For instance, dealing with the Three Body Problem it was not expected, using the Newtonian paradigm, that the problem of computing the mutual gravitational interaction of three masses was unsolvable, even when they are constrained to lie in a common plane.

A second kind is named phenomenological emergence. It relates to the need of the observer to change conceptually the model or the representation used during observation of an evolving phenomenon. An example is given by phenomena such as superconductivity, ferromagnetism or lasers which, being manifestations of collective effects, can no longer be described by resorting to the traditional models of classical Physics. Another example is given by collective behaviours such as cooperative phenomena underlying the operation of industrial districts which cannot be described by using the classical models of Economics.

A third kind is named intrinsic emergence. It relates to processes in which the occurrence of a certain behaviour is not only unpredictable, but its occurrence gives rise to profound changes in system structures such as to require a formulation of a new model of the system itself. We mention the main necessary (but not always sufficient) properties a process must have to be considered intrinsically emergent:

a) possibility of describing the interactions between the components of the system;

b) existence of intrinsic fluctuations of the behaviours of these components. They may be due to stochastic noise, chaotic behaviours or to quantum-like phenomena;

c) the system must be both thermodynamically and logically open with respect to the external environment. Such openness is needed for the survival of the intrinsically emergent coherent entities, owing to contributions from the outside world.

Table 2. Processes of Emergence compared with reference to structure and acquisition of properties.

Emergence of variable behaviours: variability of the structure is, dynamic, irregular, but coherent

Emergence of hierarchies of systemic properties: variability of the structure is not only dynamic, irregular and coherent, but also generating hierarchies of systems

Variability of the structure of a process of self-organisation is dynamic, irregular, but coherent, i.e. so detected by the observer. For instance swarms and flocks assuming variable behaviours as in presence of any suitable environmental condition. Subsequent systems are not hierarchical, but sequential and coherent in time, i.e. they display to the observer the same property.

Coherence is maintained in presence of any internal or external perturbation.

Variability of the structure of a process of self-organisation is not only dynamic, irregular and coherent, but also generating hierarchies of systems acquiring subsequent properties. For example in living matter there is emergence of systems having functionalities such as cognitive abilities. Then mind is established able to influence all the underlying levels.

Coherence relates to the modelling of the observer.

Dynamic change of structure corresponds to dynamic acquisition of properties to be suitable modelled by the observer (e.g., by DYSAM and Meta-structures)